The sum of 2xy(3x+4y−5z) and 5yz(2x−3y) is:
- A6x
2
y−8xy
2
+15y
2
z - B6x
2
y+8xy
2
−15y
2
z - C6x
2
y+8xy
2
−15y
2
z−20xyz - D6x
2
y−8xy
2
+15y
2
z+20xyz
Solution & Step-by-step Explanation
First, let us expand the two expressions:
First expression:
2xy(3x+4y−5z)=6x
2
y+8xy
2
−10xyz
Second expression:
5yz(2x−3y)=10xyz−15y
2
z
Now, find the sum of both expanded expressions:
Sum=(6x
2
y+8xy
2
−10xyz)+(10xyz−15y
2
z)
Sum=6x
2
y+8xy
2
−10xyz+10xyz−15y
2
z
Sum=6x
2
y+8xy
2
−15y
2
z
First expression:
2xy(3x+4y−5z)=6x
2
y+8xy
2
−10xyz
Second expression:
5yz(2x−3y)=10xyz−15y
2
z
Now, find the sum of both expanded expressions:
Sum=(6x
2
y+8xy
2
−10xyz)+(10xyz−15y
2
z)
Sum=6x
2
y+8xy
2
−10xyz+10xyz−15y
2
z
Sum=6x
2
y+8xy
2
−15y
2
z